Question: An electric train in Japan runs with a speed \[1.3\,{\text{Mach}}\]. It is approaching a station and...

Question

An electric train in Japan runs with a speed $1.3\,{\text{Mach}}$ . It is approaching a station and blows a whistle of frequency $88\,{\text{Hz}}$ . The frequency of the whistle heard by a stationary observer on a platform is:
A. $800\,{\text{Hz}}$
B. $1600\,{\text{Hz}}$
C. $1040\,{\text{Hz}}$
D. Insufficient data.

Answer 1

Solution

First of all, take into account the speed of the electric train. Had it been less than $1\,{\text{Mach}}$ , then it would have meant that the speed of the train is lesser than the speed of the sound.

Complete step by step solution:
In the given question, the train is running with a speed of $1.3\,{\text{Mach}}$ . The unit ${\text{Mach}}$ is used to define the ratio of speed of the source to that speed of sound in air. $1.3\,{\text{Mach}}$ is used to define that the speed of the body is ${\text{1}}{\text{.3}}$ times faster than that of speed of sound in air.
When the frequencies of the sound source and the listener are significantly smaller than the speed of sound, the Doppler effect is applicable.
In this case, the sound source is much faster than the speed of sound itself.
The particles in matter waves still have momentum, unlike vibration, light and radio waves. This momentum is acquired due to the source 's velocity. It is not feasible to apply Doppler shift to achieve the frequency of matter waves with added momentum.

Hence, the correct option is (D).

Additional information:
The Doppler effect, or Doppler shift, explains the frequency variations of something like a sound or light wave which a moving object generates in comparison to an observer. As the source approaches the viewer, waves produced from an object moving towards a viewer are compressed and triggered to an increasing frequency.

Note: While answering this question you should have a firm knowledge of Doppler’s effect along with the conditions for which it is valid. Note that the speed of the train is greater than the speed of sound itself. If the source sound velocity is higher than the sound velocity, and as such the wave front is warped due to shock waves, so the listener cannot examine the difference in frequency.